Geodesic
On the rank of random subsets of finite affine geometry
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 209-217.

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The aim of the paper is to give an effective formula for the calculation of the probability that a random subset of an affine geometry AG(r-1,q) has rank r. Tables for the probabilities are given for small ranks. The expected time to the first moment at which a random subset of an affine geometry achieves the rank r is derived.
Keywords: finite affine geometry, random matroids, hitting time 
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Kordecki, Wojciech. On the rank of random subsets of finite affine geometry. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 209-217. http://geodesic.mathdoc.fr/item/DMGT_2000_20_2_a4/

[1] C.J. Colbourn and J.H. Dinitz, The CRC Handbook of Combinatorial Designs (CRC Press, Boca Raton, 1996).

[2] W. Kordecki, On the rank of a random submatroid of projective geometry, in: Random Graphs, Proc. of Random Graphs 2 (Poznań 1989, Wiley, 1992) 151-163.

[3] W. Kordecki, Random matroids, Dissert. Math. CCCLXVII (PWN, Warszawa, 1997).

[4] W. Kordecki, Reliability bounds for multistage structures with independent components, Statist. Probab. Lett. 34 (1997) 43-51, doi: 10.1016/S0167-7152(96)00164-2.

[5] M.V. Lomonosov, Bernoulli scheme with closure, Probl. Inf. Transmission 10 (1974) 73-81.

[6] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992).

[7] B. Voigt, On the evolution of finite affine and projective spaces, Math. Oper. Res. 49 (1986) 313-327.

[8] D.J.A. Welsh, Matroid Theory (Academic Press, London, 1976).